A Detailed Derivation of the Emergent "New c" from Amplitude–Phase Coupling in the Primeon Framework (State-Function Formulation)

Superseded interpretation: This manuscript proposed an amplitude–phase stiffness ratio as an emergent causal speed. Completing the quadratic form remains mathematically valid under the stated assumptions, but that calculation does not establish a propagation speed or universal causal cone. The subsequent paper, The Causal Meaning of c: The Common Cone of the P1 Wave Equation, replaces this interpretation with a principal-symbol analysis. The origin of the spacetime causal structure and its universality across physical sectors remain open. The updated paper is in: https://doi.org/10.5281/zenodo.23516022